Reliability
From the search data
we generated the first rows of the respective matrices by programs.
Other programs took this data and generated both the orthogonal designs
and the parts of the LaTeX file used to write the paper.
The orthogonal designs were subsequently checked by a third set of programs.
Because multiple checks are involved, and because the final
check amounts to simply testing the product of a matrix
and its transpose,
we are very confident that the orthogonal designs presented on
this website are correct.
Assuming no errors have crept in after the electronic submission
of the paper(s) there should be no errors in
the tables in the published papers either.
While the searches were done carefully,
the level of confidence in the completeness of the search
cannot be established and is lower in the following sense.
It is possible that additional sequences of amicable type
could have been found from the
input data (of order 20 or order 28) sequences.
In fact,
different sequences (of order 20 or 28) of the same type
may lead to additional amicably generated sequences (of order 40 or 56).
Accordingly we make no claim that the searches were exhaustive.
Since sequences were found for all types using negacyclic matrices
or doubling in the cases were amicability failed,
this is not a major concern.